Simulating the central limit theorem

Abstract. Understanding the central limit theorem is crucial for comprehending
parametric inferential statistics. Despite this, undergraduate and graduate
students alike often struggle with grasping how the theorem works and why researchers
rely on its properties to draw inferences from a single unbiased random
sample. In this article, I outline a new command, sdist, that can be used to
simulate the central limit theorem by generating a matrix of randomly generated
normal or nonnormal variables and comparing the true sampling distribution standard
deviation with the standard error from the first randomly generated sample.
The user also has the option of plotting the empirical sampling distribution of
sample means, the first random variable distribution, and a stacked visualization
of the two distributions.